diff --git a/src/frontend/src/binder/bind_context.rs b/src/frontend/src/binder/bind_context.rs
index 6a08e9393206..02dbc6a28bc1 100644
--- a/src/frontend/src/binder/bind_context.rs
+++ b/src/frontend/src/binder/bind_context.rs
@@ -81,12 +81,12 @@ pub struct LateralBindContext {
 /// WITH RECURSIVE t(n) AS (
 /// # -------------^ => Init
 ///     VALUES (1)
-/// # ----------^ => BaseResolved (after binding the base term)
 ///   UNION ALL
-///     SELECT n+1 FROM t WHERE n < 100
-/// # ------------------^ => Bound (we know exactly what the entire cte looks like)
+///     SELECT n + 1 FROM t WHERE n < 100
+/// # --------------------^ => BaseResolved (after binding the base term, this relation will be bound to `Relation::BackCteRef`)
 /// )
 /// SELECT sum(n) FROM t;
+/// # -----------------^ => Bound (we know exactly what the entire `RecursiveUnion` looks like, and this relation will be bound to `Relation::Share`)
 /// ```
 #[derive(Default, Debug, Clone)]
 pub enum BindingCteState {
diff --git a/src/frontend/src/binder/query.rs b/src/frontend/src/binder/query.rs
index 9ab1918776fb..dd6ff9f36b81 100644
--- a/src/frontend/src/binder/query.rs
+++ b/src/frontend/src/binder/query.rs
@@ -284,6 +284,7 @@ impl Binder {
 
     fn bind_with(&mut self, with: With) -> Result<()> {
         for cte_table in with.cte_tables {
+            // note that the new share id is generated here
             let share_id = self.next_share_id();
             let Cte { alias, query, .. } = cte_table;
             let table_name = alias.name.real_value();
diff --git a/src/frontend/src/optimizer/plan_node/logical_recursive_union.rs b/src/frontend/src/optimizer/plan_node/logical_recursive_union.rs
index 0467113b515e..376e30ca3a19 100644
--- a/src/frontend/src/optimizer/plan_node/logical_recursive_union.rs
+++ b/src/frontend/src/optimizer/plan_node/logical_recursive_union.rs
@@ -22,9 +22,7 @@ use super::expr_visitable::ExprVisitable;
 use super::generic::GenericPlanRef;
 use super::utils::{childless_record, Distill};
 use super::{
-    generic, ColPrunable, ColumnPruningContext, ExprRewritable, Logical, PlanBase, PlanTreeNode,
-    PredicatePushdown, PredicatePushdownContext, RewriteStreamContext, ToBatch, ToStream,
-    ToStreamContext,
+    gen_filter_and_pushdown, generic, ColPrunable, ColumnPruningContext, ExprRewritable, Logical, PlanBase, PlanTreeNode, PredicatePushdown, PredicatePushdownContext, RewriteStreamContext, ToBatch, ToStream, ToStreamContext
 };
 use crate::binder::ShareId;
 use crate::error::Result;
@@ -97,10 +95,10 @@ impl ExprVisitable for LogicalRecursiveUnion {}
 impl PredicatePushdown for LogicalRecursiveUnion {
     fn predicate_pushdown(
         &self,
-        _predicate: Condition,
-        _ctx: &mut PredicatePushdownContext,
+        predicate: Condition,
+        ctx: &mut PredicatePushdownContext,
     ) -> PlanRef {
-        unimplemented!("recursive CTE not supported for predicate_pushdown of LogicalRecursiveUnion")
+        gen_filter_and_pushdown(node, filter_predicate, pushed_predicate, ctx)
     }
 }